A special feature of the genus two case is the Narasimhan-Ramanan isomorphism, see [1]}, which implies that \(S^k(H^{(1)}_X) = H^{(k)}_X\)  where \(S^k\)  denotes the \(k^{\mathrm {th}}\)  symmetric power of a vector space. Beauville showed an isomorphism, for all \(g \geqslant 2\) , between \(\mathbb {P}H^{(1)}_X\)  and \(\mathbb {P}F_g\) , where \(F_g\)  is the vector space of complex valued functions on the group \(\mathbb {Z}_2^g\) , see [2]}. Moreover, this isomorphism only depends on the choice of a level two theta structure on \(X\) .
